$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 3x - 2$ and $ BC = 6x - 11$ Find $AC$.
A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {3x - 2} = {6x - 11}$ Solve for $x$ $ -3x = -9$ $ x = 3$ Substitute $3$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 3({3}) - 2$ $ BC = 6({3}) - 11$ $ AB = 9 - 2$ $ BC = 18 - 11$ $ AB = 7$ $ BC = 7$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {7} + {7}$ $ AC = 14$